Effective wall-normal height of the energetic nonlinear source

Determine which combination of effective nonlinear-source height and break-frequency prefactor is consistent with the wall-pressure spectrum, distinguishing a mid-layer source at approximately \(y_{Q,\mathrm{eff}}/\delta=0.5\) with \(C_{bQ}^r=1\) from a log-layer source with \(y_{Q,\mathrm{eff}}/\delta\lesssim 0.1\) and \(C_{bQ}^r=O(2\pi)\).

Background

The model relates the outer spectral break to the effective wall-normal location of the energetic nonlinear source through the convection velocity, the boundary-layer thickness, and an undetermined order-one prefactor. Different choices of this prefactor imply substantially different source heights.

The elliptic Green-function attenuation strongly suppresses contributions from sources located deep in the layer, but the wall spectrum alone does not determine whether the inferred break reflects a mid-layer source with a small prefactor or a lower log-layer source with a larger aspect-ratio prefactor. Wall-normal source statistics, particularly from rough-wall DNS, are needed to resolve the ambiguity.